# Alternate form of the Residue theorem?

I'm brushing up on my complex for an upcoming qual, and one of the questions had me use an alternate form of the residue theorem:

$$\oint_{\partial \Omega} \frac{f(\zeta)}{z-\zeta} d \zeta = 2 \pi i \sum_{j=1}^{n}\text{Res}(f,z_j)$$

for $f$ meromorphic on a bounded, star-shaped domain $D$ with boundary $\Gamma$, and $z \in \Omega$. I'm pretty sure it involves that the index of any path is one, but I can't figure out how to put it together.

-
You have several things which are a bit confusing. You have a domain $D$ and also $\Omega$ in which you defined $D$ but not $\Omega$. In contrast, you used $\Omega$ in the question but not $D$. Am I correct in assuming that your $D$ and $\Omega$ are the same? –  EuYu Nov 11 '12 at 18:53